Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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        <div xml:id="echoid-div205" type="section" level="1" n="132">
          <pb o="85" file="0105" n="105" rhead="LIBER I."/>
          <p style="it">
            <s xml:id="echoid-s2106" xml:space="preserve">Tres autem proximæ Propoſitiones etiam in meo Speculo Vſtorio de-
              <lb/>
            ſcriptæ fuerunt, cum & </s>
            <s xml:id="echoid-s2107" xml:space="preserve">ibi ijſdem indigerem, has verò hic repetere
              <lb/>
            volui, vt qui meum illud Speculum non viderunt, etiam ijſdem potiri
              <lb/>
            poſſint: </s>
            <s xml:id="echoid-s2108" xml:space="preserve">Aliqua tamen ex infraſcriptis nunc ex Archimede, & </s>
            <s xml:id="echoid-s2109" xml:space="preserve">eiuſdem
              <lb/>
            Commentatoribus ſumemus, vt iam oſtenſa, ne has demonſtrationes, quæ
              <lb/>
            apud præfatos Auctores videri poſſunt, fruſtra repetamus.</s>
            <s xml:id="echoid-s2110" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div206" type="section" level="1" n="133">
          <head xml:id="echoid-head144" xml:space="preserve">THEOREMA XXXVIII. PROPOS. XLI.</head>
          <p>
            <s xml:id="echoid-s2111" xml:space="preserve">SI ſphęra, vel ſphęroides, conoides parabolicum, vel hy-
              <lb/>
            perbolicum planis ſecentur ad axem rectis, communes
              <lb/>
            ſectiones erunt circuli diametros in eadem figura ducta per
              <lb/>
            axem (quæ eſt illa, quę per reuolutionem creat dictum ſoli-
              <lb/>
            dum) ſitas habentes.</s>
            <s xml:id="echoid-s2112" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2113" xml:space="preserve">Patet hæc Propoſitio, nam ſupradicta ſunt ſolida rotunda, na-
              <lb/>
              <note position="right" xlink:label="note-0105-01" xlink:href="note-0105-01a" xml:space="preserve">Defin. 6.
                <lb/>
              34. huius.</note>
            ſcuntur .</s>
            <s xml:id="echoid-s2114" xml:space="preserve">n. </s>
            <s xml:id="echoid-s2115" xml:space="preserve">ex reuolutione figurarum circa axem.</s>
            <s xml:id="echoid-s2116" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div208" type="section" level="1" n="134">
          <head xml:id="echoid-head145" xml:space="preserve">THEOREMA XXXIX PROPOS. XLII.</head>
          <p>
            <s xml:id="echoid-s2117" xml:space="preserve">SI conoides parabolicum plano ſecetur non quidem per a-
              <lb/>
            xem, neque æquidiſtanter axi, neque ad rectos angulos
              <lb/>
            cum axe, communis ſectio erit ellipſis, diameter verò ipſius
              <lb/>
            maior erit linea concepta in conoide ab interſectione facta
              <lb/>
            planorum, eius ſcilicet, quod ſecat figuram, & </s>
            <s xml:id="echoid-s2118" xml:space="preserve">eius, quod
              <lb/>
            ducitur recto per axem ad planum ſecans, minor verò diame-
              <lb/>
            ter æqualis erit diſtantiæ linearum ductarum æquidiſtanter
              <lb/>
            axi ab extremis diametri maioris.</s>
            <s xml:id="echoid-s2119" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2120" xml:space="preserve">Hæc oſtenditur ab Archimede lib. </s>
            <s xml:id="echoid-s2121" xml:space="preserve">de Conoidibus, & </s>
            <s xml:id="echoid-s2122" xml:space="preserve">Sphæroidi-
              <lb/>
            bus p. </s>
            <s xml:id="echoid-s2123" xml:space="preserve">13.</s>
            <s xml:id="echoid-s2124" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div209" type="section" level="1" n="135">
          <head xml:id="echoid-head146" xml:space="preserve">THEOREMA XL. PROPOS. XLIII.</head>
          <p>
            <s xml:id="echoid-s2125" xml:space="preserve">SI conoides hyperbolicum plano ſecetur coincidente in
              <lb/>
            omnia conilatera conoides compræhendentis non recto
              <lb/>
            ad axem; </s>
            <s xml:id="echoid-s2126" xml:space="preserve">ſectio erit ellipſis, diameter verò maior ipſius erit
              <lb/>
            concepta in conoide à ſectione facta planorum, alterius </s>
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